3 Processing Dissipation Rates obtained aboard AUV Abyss
3.1 Inferring Dissipation Rates from Velocity Shear Microstructure
but this has been limited to the upper ocean (Levine and Lueck, 1999;Lueck et al., 2002;Thorpe et al., 2003;Goodman et al., 2006;Steele et al.). The detection limits of these studies were similar to the one of the AUV-MR system described in this thesis. In the following, the general method of inferring dissipation rates from ve-locity shear microstructure and the specific challenges arising from the operation of the MR on AUV Abyss are introduced. Two methods of inferring dissipation rates are compared and the subsequent noise and errors are discussed.
3.1 Inferring Dissipation Rates from Velocity Shear Microstructure
The dissipation rate of turbulent kinetic energy () may be computed from velocity shear data by integration of shear spectra (Φ) under the assumption of isotropic turbulence (Taylor, 1935; Oakey, 1982):
= 7.5ν
* δw δx
!2+
= 7.5ν
Z ∞ 0
Φ dk, (3.1)
withνbeing the kinematic viscosity,kthe wavenumber, andD(δw/δx)2E represent-ing the variance of the fluctuations of the velocity perpendicular to the direction of travel. Following Gargett et al.(1984) andYamazaki and Osborn (1990), isotropy may be assumed if > 200·νN2, with N being the buoyancy frequency. Using N2 < 2.3·10−61/s2 and ν = 1.6·10−6m2/s as determined from CTD profiles, a conservative estimate for isotropy conditions is >8·10−10W/kg which is on the order of the noise level (Section 3.3). Thus, isotropy can be assumed for dissipation rates reported throughout this thesis.
3 Processing Dissipation Rates obtained aboard AUV Abyss
It is commonly assumed that a velocity shear spectrum Φ has the shape of the uni-versal Nasmyth spectrum determined by Nasmyth (1970) and reported by Oakey (1982). As described in Section 2.3.2, accelerometer data of the MR showed el-evated vibrations originating from the AUV and the mounting of the MR. The wavenumber range of these vibrations are collocated within the wavenumber band (k band) occupied by turbulent fluctuations. Thus, their contributions to shear variance have to be eliminated prior to the integration of the shear spectra. Here, two different procedures were used to achieve this requirement introduced below.
Facing the same problem as described above, Goodman et al. (2006) developed a filter to remove microstructure shear contributions due to vibrations originat-ing from a shallow-water REMUS AUV, that is now standardly implemented into microstructure data processing even for free-falling microstructure profilers (Fer et al., 2014). The filter removes portions of the shear spectrum Φ that are co-herent with the three dimensional acceleration signals recorded simultaneously to the shear signal, resulting in a filtered spectrum (φf). The untreated spectrum is referred to as raw spectrum (φr) hereafter.
The microstructure shear time series were divided into 6 s long segments for spec-tral analysis. A fast Fourier transform (FFT) segment length of 2 s was chosen with 50 % overlap. Thus, each estimate of the dissipation rate is based on spectral estimates from five 2 s long ensembles that were detrended and Hanning windowed prior to spectral decomposition (Blackman and Tukey, 1958; Harris, 1978). The relatively long interval of 6 s is necessary for an optimal use of the Goodman filter (Goodman et al., 2006).
Two examples of typical shear spectra, one corresponding to elevated and one corresponding to low dissipation rates of turbulent kinetic energy, are presented (Fig. 3.1). In the high turbulence case (Fig. 3.1a), the filtered and raw spectrum compare reasonably well for wavenumbers larger than 10 cpm (cpm - cycles per me-ter). However, in the low turbulence case (Fig. 3.1b), the difference betweenφf and φr of up to two orders of magnitude for the samek band (k >10 cpm) is distinct, indicating elevated contributions from the vibrations of the instrument package.
In both cases, power spectral densities for the k band between 10 and 15 cpm are least affected by vibrations, independent from the turbulence level (Fig. 3.1). On the contrary, spectral densities for the k band between 3 and 10 cpm are most strongly affected by the instrumental vibrations. In this k band, elevated differ-ences betweenφf and φr even prevail in the elevated turbulence case.
The vibrations induced from the instrument package showed comparable spectral energy levels for both turbulence environments (Fig. 3.1) as well as in the average accelerometer spectra (Fig. 2.4). This indicates the vibrations to be independent from the turbulent environment at least for the range of turbulence encountered over the course of this study.
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3.1 Inferring Dissipation Rates from Velocity Shear Microstructure Visual inspection of shear spectra from the different dives and regions indicated that the spectral shape of Φf compares well to the shape of the universal Nasmyth spectrum for wavenumbers larger than 10 cpm when the signal is above the shear noise level (about 1·10−61/(s2cpm)). For smaller wavenumbers (k < 10 cpm), spectral densities of the filtered spectrum are attenuated too strongly by the Good-man filter. In particular, this is most pronounced fork <2 cpm, where acceleration spectra show only weak instrumental vibrations (Figs. 2.4 and 3.1). The reason for this behavior could not be fully assessed. In part, the attenuation could be due to movement of the instrument package induced by turbulent motions of the ocean on length scales that will lead to coherence between the acceleration and the shear signals in this k range (Goodman et al., 2006). Using Φf would thus underestimate the turbulent shear contributions in this k range.
In order to avoid both, the use of the attenuated wavenumber band (k < 2 cpm) and the wavenumber band of particularly elevated instrumental vibrations (2 cpm to 10 cpm), the low noisekband (10 cpm to 15 cpm) is used as origin for estimating dissipation rates of turbulent kinetic energy. Two different methods are introduced to compute the dissipation rate detailed below.
100 101 102
power spectral density [1/s2 /cpm]
ε hybrid = 4.8e−08 [W/kg]
(a)Example for elevated turbulence.
100 101 102
power spectral density [1/s2 /cpm]
ε hybrid = 5.5e−10 [W/kg]
(b) Example for low turbulence.
Figure 3.1: Example velocity shear spectra (colored lines) for one segment of el-evated turbulence (a) and one segment of low turbulence environment (b). Spec-tra of the 3-dimensional acceleration are also shown (Ax- the direction of Spec-travel, Ay-directed to port, Az-directed upward). The dissipation rate estimate for each segment is given in the upper right corner of each panel. The corresponding Nas-myth spectrum is indicated by the thick black, dashed line. The gray lines with dots indicate the Nasmyth spectra for =10−10,10−9,10−8,10−7W/kg.
3 Processing Dissipation Rates obtained aboard AUV Abyss